My favorite facility was Battle Factory, as we were able to rent Pokémon with computer-generated move-sets and whatnot, which I personally found to be quite adventurous. It tested you as to how good you are as an in-game battler in general, and how well you're able to utilize Pokémon. Due to Factory being my most favorite, Nolan has got to be my favorite brain as well, even though it might sound a little biased. I've went up against him a few times, but sadly, was never able to have him defeated, as his team was assembled pretty tightly, so to speak. Was close at one point, but did not manage to pull it off successfully, unfortunately. Back then, I wasn't too great with Pokémon strategies, either, which is another reason as to why.
As for second favorite, I'd say Pike Queen Lucy. Love her appearance (to me, she looks very beautiful), and when it came to battling, she was sort of challenging as well; have always been able to put up a good match.